Question

A charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is maximum, is :

• A. $Q$
• B. $\frac{3Q}{4}$
• C. $\frac{Q}{2}$
• D. $\frac{Q}{3}$

Answer 1

The correct option is C $\frac{Q}{2}$

Let the two charges are separated by a distance $r$

$\therefore$ Coulomb force $F=\frac{Kq(Q-q)}{r^2}=\frac{K(qQ-q^2)}{r^2}$, where $K=\frac{1}{4\pi {ϵ}_o}$

For the force to maximum, $\frac{dF}{dq}=0$

$\therefore$ $\frac{K}{r^2}\times (Q-2q)=0$

or, $Q-2q=0$ $⟹q=\frac{Q}{2}$